This is exactly right! I typically walk also but ride when I play with my step-dad who has a knee issue and can't walk 18 so we ride. A month ago it was just us and three women walking were pushing us playing lightning fast so we let them go. Just cause we have a cart doesn't mean we are faster as my step-dad just moves slower. I've walked countless times with friends and played up the ass of a group of cart riders who just play slow. There is nothing wrong with slow play as long as they know it and let people play through, be polite and not a dick about it and as to play through. Some people know they are slow and will let you go through.
People should be able to booze up all they want and enjoy your day, your paying for it. As long as it doesn't interfere too much with everyone else. Nobody is playing for money or anything so just enjoy the day.